Lunar-Solar Perturbations of an Earth Satellite

Abstract

The influence of the sun and moon on the orbit of a near satellite of the earth is investigated, and it is shown that the principal effect is a precession of the orbit plane about the pole of the ecliptic, analogous to the precession of the equinoxes. The precessional rate increases with orbit size and eccentricity and decreases with orbit inclination to the equator. For orbits close to the earth the lunar-solar precessional motion is only about 10−4 that due to the earth's oblateness. Radial perturbations resulting from the attractions of the sun and moon are similarly extremely small, being of the order of one meter. The induced radial oscillations exhibit twice the frequency of the satellite's orbital motion around the earth, analogous to the twice daily motion of the tides. To second-order terms in the orbit eccentricity the expressions derived herein are in exact agreement with the astronomical treatments for the special case of the perturbations of the moon's orbit due to the sun.